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 A356114 Number of irreducible permutations of n with partition type [2, 1, 1, ..., 1] (with '1' taken n - 2 times). 1
 0, 0, 0, 2, 9, 24, 55, 118, 245, 500, 1011, 2034, 4081, 8176, 16367, 32750, 65517, 131052, 262123, 524266, 1048553, 2097128, 4194279, 8388582, 16777189, 33554404, 67108835, 134217698, 268435425, 536870880, 1073741791, 2147483614, 4294967261, 8589934556, 17179869147 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Irreducible permutations in connection with partition types are discussed in A356262. Compare with the subdiagonal of A356263. LINKS Index entries for linear recurrences with constant coefficients, signature (4,-5,2). FORMULA a(n) = 2^n - n - 3 for n >= 3. a(n) = Eulerian1(n, n - 2) - 2 for n >= 3. G.f.: x^3*(2*x^2 - x - 2)/((x - 1)^2*(2*x - 1)). a(n) = A356263(n, n - 2) for n >= 2. EXAMPLE a(4) = 9 = card({2413, 2431, 3142, 3241, 3421, 4132, 4213, 4231, 4312}). The other two permutations of type [2, 1, 1], 1432 and 3214, are reducible. That there are 11 permutations of type [2, 1, 1] we know from Euler's triangle A173018 or from its refined form A355777. MAPLE seq(`if`(n < 3, 0, combinat:-eulerian1(n, n - 2) - 2), n = 0..34); CROSSREFS Cf. A356262, A356263, A355777, A079500. Sequence in context: A023662 A131357 A274543 * A079997 A351252 A275260 Adjacent sequences: A356111 A356112 A356113 * A356115 A356116 A356117 KEYWORD nonn,easy AUTHOR Peter Luschny, Aug 01 2022 STATUS approved

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Last modified March 31 08:37 EDT 2023. Contains 361645 sequences. (Running on oeis4.)